Infinite Pursuits @infinitepursuits - Tumblr Blog

Some mathematicians claim they can visualize R^4, or even higher-dimensional spaces. I think this is probably possible for the human mind to do, in principle; the human mind often proves surprisingly flexible. But I think it probably takes a lot of concerted practice, and because you are stretching your mind beyond its intended limits in a purely-internal, imaginative way with no external reference points to check against, I think it probably has some things in common with certain types of meditative practice.

It's also common to hear mathematicians say that if humans had visual intuition for dimensions higher than 3, higher-dimensional geometry may have advanced much farther, since visual intuition is so often crucial in thinking of proofs.

So, ok, I suspect that AI will obviate the utility of this before it could ever have the chance to get off the ground, but this all makes me imagine a world where techniques for learning to visualize higher dimensions are well-known and practiced, and have become a functional necessity for being a working geometer in higher-than-3-dimensions. And these techniques require a lot of persistent practice and training, which (by the nature of the thing) is hard to precisely communicate to students. So part of becoming a geometer involves training in what is basically a meditative practice, where, à la Zen, much of the process involves not directly teaching the student but giving them prompts and mental exercises that are meant to trigger internal, incommunicable revelation. But instead of enlightenment it's geometric intuition. And so if we're getting a math PhD in, say, differential equations or something, it's mostly like it is today. But if your PhD is in low-dimensional topology there's like a whole monastic apprenticeship style thing that just comes along with it. People sometimes drive themselves insane. People sometimes drive themselves insane.

mobiusstripearthtruther-deactiv

"double," "triple" <- normal words for describing multiplication

"sextuple" <- some kind of perverted data type

theconcealedweapon

duckbunny

your twenties are not "late" to start hrt. that is a normal time to start hrt. your thirties are also a normal time to start hrt. your seventies are pretty late to start hrt, but not too late. like, statistically, that's at the end of the curve. but if you are not dead, it is not too late for hrt.

These two fire extinguishers at my work

edge-complains-and-loves-art

Had to draw them

fipindustries

the real magic of arnold schwarzenegger was that movies in the 90's kept insisting this giant austrian man with the face of a mountainside and this really thick accent was an average all-american suburban family man, and we believed it.

phaeton-flier

See the thing is despite looking like an attempt to make Bratwurst without a grinder, he can act like some put upon schlub barely keeping it together. You see him run around trying to get a Turboman Action Figure, you believe that he has the soul of a dweeb

xenosaurus

it’s a shame more vampire media doesn’t pull from vampire bat behavior because they’re such sweeties. they can only survive their incredibly specialized diet because bats will share blood with colony members that didn’t find a meal! there’s evidence that suggests the donors sometimes initiate this behavior themselves by approaching hungry bats! the colonies are mostly harems of females with a few males but they’ve been observed letting unrelated males in when it gets cold so they can all stay warm! cute little social critters!

dizzyhslightlyvoided

"Men Aren't Better Than Women: Both Genders Are Inferior To Me" is a 1991 book by Dr. Ivo Robotnik (better known for other work). Though its primary purpose is clearly to stroke the author's own ego, it is generally regarded as a comprehensive, well-constructed, and accessible work of contemporary feminist theory, and is still commonly-cited to this day.

Most of the critical complaints have been about the tone; in a review from 2005, Professor Victoria of Spagonia University said, "The constant self-aggrandizement undercuts the idea that its subject ought to be taken seriously. Also, wasn't the 'feminist' line from the Sonic Heroes manual a mistranslation of 'womanizer'?"

In 2026, Dr. Robotnik released a new edition updated for the preceding 35 years of developments in feminism, with the subtitle changed from "Both Genders" to "All Genders."

demilypyro

to become a girl and have things done to you..... this is a dream shared by all I think.... even when I was a boy and I had a girlfriend..... truly, I was jealous! I was jealous of her position! I was jealous of her body! mine had no appeal at all! to be a girl just carries so much more appeal..... these boobs are for me alone

demilypyro

I think that's when I figured it out actually.... I lost my virginity, but it was so depressing.... I didn't like it at all..... my body was so ugly and hers was so pretty..... I wanted a body like hers for myself..... I wanted to feel good about my body.... becoming a girl was the only way.... you get it, right? you get it, right?

thisarenotarealblog

heraldic-thunderbolt

You ever think about what differentiates us from the enemy?

m3n4c3v35537

possession of the mandate of heaven, surely

blastdamage

the paris catacombs are 1000x more fucked up than i imagined

blastdamage

did you know the cops once found a fully functioning movie theater with a well-stocked bar inside the catacombs and they when they tried to go back later to formally investigate it was completely emptied out save for a note that read "don't search for us"

biggest-gaudiest-poltergeist

Underground french cinema

npd-vriska

my little bro is part of the catacombs community and yeah, it's basically a fully autonomous society! enough that when my bro goes in on a friday night, they don't come out until monday for work- sometimes longer if they took days off.

some of the rooms have fully stocked pantries with cooking equipment, some have movies like the one described above, some have books you're allowed to just take but people always put back- every day people bring things from the outside. artists often set up galleries there. there are rooms with mattresses and hammocks set up for people to sleep. one of the room is just a place where people leave shoes for the fun of it.

this is Known, it's not a secret by any means. the catacombs are as big as paris itself, and people live there just as people live above. it's wonderful when you think about it.

npd-vriska

A little update! My little bro is now my little sister. Please don't misgender her :)

sadfaceclown

Ashley also known as squidkid1111 took their own life after facing bullying from the cosplay community due to them being a cosplayer of color. Rest in peace.

uptownlowdown

a reminder that racism in fandom/nerd/hobby spaces has real life consequences, and is not something you can simply filter or block out of existence. people whine about “serious” topics ruining fandom, meanwhile Black fans are routinely belittled and harassed simply for existing in these spaces.

rest in eternal power, ash. i’m so sorry this happened to you.

creatingblackcharacters

Also, because they were* a Black cosplayer. Not just "of color", they're not synonymous. Say Black, please. Harassment for cosplaying while Black comes from nonblack fans of color, too. Many Black cosplayers will tell you of the baffling experience.

*correction: I heard they went by she/they but the post says they. My apologies.

paper-mario-wiki

Visit Original Link

You would not believe your flies if ten million fire eyes lit up the world as I feel asleels.

Cuz they’d fill they fill the open eyes and leave sockhops everywhere you’d think me rude but I would just stand and

dance.

I’d like to make myself a fly. Planet eeeeeaaaaaaaaaaaaaaaaaaarth Sloooooooooowlyyyylle.

It’s hard to say that I’d rather Seal the deal when I’m a 𝕤𝕟𝕒𝕚𝕝. Cuz everything is never as it meeeeeeeeeeeeeeemmmmmmees.

Cuz I get a thousand bugs from ten thousand lightning hugs as they try to teach me how to fuck.

a fox trot above my hugs a sockhop beneath my 𝖇𝖆𝖑𝖑𝖘 the disco bug is just hanging by a thread

inkdot-deactivated20200219

no shit.

This weekend I was told a story which, although I’m kind of ashamed to admit it, because holy shit is it ever obvious, is kind of blowing my mind.

A friend of a friend won a free consultation with Clinton Kelly of What Not To Wear, and she was very excited, because she has a plus-size body, and wanted some tips on how to make the most of her wardrobe in a fashion culture which deliberately puts her body at a disadvantage.

Her first question for him was this: how do celebrities make a plain white t-shirt and a pair of weekend jeans look chic? She always assumed it was because so many celebrities have, by nature or by design, very slender frames, and because they can afford very expensive clothing. But when she watched What Not To Wear, she noticed that women of all sizes ended up in cute clothes that really fit their bodies and looked great. She had tried to apply some guidelines from the show into her own wardrobe, but with only mixed success. So - what gives?

His answer was that everything you will ever see on a celebrity’s body, including their outfits when they’re out and about and they just get caught by a paparazzo, has been tailored, and the same goes for everything on What Not To Wear. Jeans, blazers, dresses - everything right down to plain t-shirts and camisoles. He pointed out that historically, up until the last few generations, the vast majority of people either made their own clothing or had their clothing made by tailors and seamstresses. You had your clothing made to accommodate the measurements of your individual body, and then you moved the fuck on. Nothing on the show or in People magazine is off the rack and unaltered. He said that what they do is ignore the actual size numbers on the tags, find something that fits an individual’s widest place, and then have it completely altered to fit. That’s how celebrities have jeans that magically fit them all over, and the rest of us chumps can’t ever find a pair that doesn’t gape here or ride up or slouch down or have about four yards of extra fabric here and there.

I knew that having dresses and blazers altered was probably something they were doing, but to me, having alterations done generally means having my jeans hemmed and then simply living with the fact that I will always be adjusting my clothing while I’m wearing it because I have curves from here to ya-ya, some things don’t fit right, and the world is just unfair that way. I didn’t think that having everything tailored was something that people did.

It’s so obvious, I can’t believe I didn’t know this. But no one ever told me. I was told about bikini season and dieting and targeting your “problem areas” and avoiding horizontal stripes. No one told me that Jennifer Aniston is out there wearing a bigger size of Ralph Lauren t-shirt and having it altered to fit her.

I sat there after I was told this story, and I really thought about how hard I have worked not to care about the number or the letter on the tag of my clothes, how hard I have tried to just love my body the way it is, and where I’ve succeeded and failed. I thought about all the times I’ve stood in a fitting room and stared up at the lights and bit my lip so hard it bled, just to keep myself from crying about how nothing fits the way it’s supposed to. No one told me that it wasn’t supposed to. I guess I just didn’t know. I was too busy thinking that I was the one that didn’t fit.

I thought about that, and about all the other girls and women out there whose proportions are “wrong,” who can’t find a good pair of work trousers, who can’t fill a sweater, who feel excluded and freakish and sad and frustrated because they have to go up a size, when really the size doesn’t mean anything and it never, ever did, and this is just another bullshit thing thrown in your path to make you feel shitty about yourself.

I thought about all of that, and then I thought that in elementary school, there should be a class for girls where they sit you down and tell you this stuff before you waste years of your life feeling like someone put you together wrong.

So, I have to take that and sit with it for a while. But in the meantime, I thought perhaps I should post this, because maybe my friend, her friend, and I are the only clueless people who did not realise this, but maybe we’re not. Maybe some of you have tried to embrace the arbitrary size you are, but still couldn’t find a cute pair of jeans, and didn’t know why.

life-in-a-monospace-typeface

Everyone Should Know How To Do Taguchi Experiments

Empiricism is an important virtue; it's great to try things and find what works for you, and there's a noble tradition of people doing that and blogging about it. We should be doing this more.

The problem is that experimenting on yourself can be pretty slow and tricky and inconvenient.

This post is about Taguchi arrays, which fix that by allowing you to get much more useful information from far fewer experiments. The method is commonly used in industry for process optimisation, but it isn’t complicated and is very easy to apply to DIY experiments. (Thanks to NightHawkInLight for making me aware of this!)

The default way kind of sucks

Suppose you're wondering what will work best to improve your sleep. You've got one of those sleep tracker devices that gives you an integrated Sleep Quality Score, so you've got a clear metric to optimise. Let's do some empiricism!

Now, what interventions to test? A lot of people say melatonin is good. Apparently 0.3mg is the ideal, but maybe 1mg works better, and it's more commonly available. Other people swear by magnesium. You can get magnesium glycinate easily, but some say magnesium l-threonate is better, although it's more expensive. You've heard exercising helps, but is cardio or strength better? And you've got some of those blue light blocking glasses, but they look kind of goofy. There’s a ton of things to test.

One thing at a time

The big piece of accepted wisdom here is to only change one thing at a time. If you change more than one thing and your sleep gets better, you won't know which thing did it. Or, one thing you change might help and the other might make things worse, so they cancel each other out and you learn nothing.

Changing one thing at a time, we need at least 8 experiments:

Baseline

0.3mg Melatonin

1mg Melatonin

Magnesium glycinate

Magnesium l-threonate

Cardio

Strength

Goofy glasses

In principle we could do this in 8 days, just trying each thing once.

But that's going to be really noisy. Just one measurement per item is hardly going to tell us anything; we should try each thing on more than one night to get more signal. Maybe do each one for two or three days? That's 16 or 24 days, which is kind of a lot. Give each thing a week and that’s 2 months of experimentation.

And also, we care about finding a good overall setup, not just which individual things work. Probably there are some interactions here, like, what if magnesium works really well, but only if you also exercise? We'd never find out using this experiment.

Test everything?

To really know, we'd want to try every combination. So, 3 levels of melatonin (none, 0.3mg, 1mg), times 3 options for magnesium (none, glycinate, l-threonate), times 3 exercise options (none, cardio, strength), times 2 for red glasses (yes or no), means... 54 days, to try each thing once. That's not great.

There's got to be a better way!

This is where Taguchi Arrays, aka Orthogonal Arrays come in!

You go to an online Taguchi array generator like this one, add in your factors and their levels, and it spits out something like this:

Before you start, it’s a good idea to randomly shuffle the order of the rows, so secular changes or cumulative effects don’t bias things.

Then you go through the rows one night at a time. Each night you follow the protocol listed, and each morning you record your Sleep Score for that protocol.

Now to analyse the results. The genius of orthogonal arrays is that for any pair of factors, every possible combination of their levels appears the same number of times. This means that you can safely compare averages.

So if for example we want to know how magnesium glycinate compares with magnesium l-threonate, we can take the average of the sleep scores of nights we took glycinate, and the average of nights where we took l-threonate, and just see which is better. This is safe to do, because all the other variables are equally represented in those sets, so they won't bias things. You can go through and check - the 3 glycinate nights have one of each of the melatonin levels, and one of each of the exercise levels, and two have glasses and one doesn't, and the exact same is true of the L-threonate nights, and of the "no magnesium" nights. And this nice property is also true for all of the possible values of all other pairs of factors.

So using just 9 nights of experiments (just one more than the original 8 night experiment which told us very little), we get at least three nights of data to average together for each level of each factor, rather than just one! And we're testing all possible combinations of levels for each pair of factors at least once. With just these 9 experiments, we can find out a huge amount of information, almost as much as we'd get from the full 54-day factorial experiment!

Limitations

Now, this works best for situations where you expect the result to be approximately a linear combination of the factors, with only simple interactions between pairs of factors. For example, if there were some major interaction between three factors, like if melatonin worked wonderfully but only if you do cardio and also don't wear light-blocking glasses, this wouldn't catch that. But real life experiments tend not to have much of that kind of thing.

And of course if you have a situation like, magnesium only starts to help with sleep on the third night in a row you take it, this won’t detect that. But that’s a problem with using ‘sleep score on the same night’ as the metric, not an issue with Taguchi methods.

I hope that this easy to use experimental design method gets widespread adoption. It really lowers the bar for getting useful information from DIY experiments. Try it for yourself!

life-in-a-monospace-typeface

The True Megagon and The Thai Wizard

Sometimes I’ll get a great comment on one of my videos - a comment that really gets what I’m talking about and raises interesting points - and I’ll think “Oh awesome, a new cool person, I should try to bring them in and introduce them to people and so on”, and then I find it’s the alt account of someone I’ve known for years.

This is often the way when I find something great that’s relevant to my specific interests. When I go to see who’s responsible, I’m slightly disappointed to find that it was done by someone I already know.

The Megagon

A Megagon is a polygon with a million sides. They're sometimes used as an example in philosophical discussions, because it's basically a circle for any practical purpose, but it's importantly, mathematically, very much not a circle. It's an example of a well defined concept that nonetheless can't be visualised.

Wikipedia has a nice page about the megagon, from which you can learn, amongst other things, that if you made a megagon the size of the Earth, the edges would be about 40 metres long, and it would be very hard to notice the 0.00036 degree angle between adjacent sides.

The Treachery of Images

But, thanks to Chana Messinger (inventor of the term "Steel-man"), and Rob Bensinger, I came to learn a very disturbing fact about that wikipedia page.

The image used to represent the megagon, a shape whose main claim to noteworthiness is that it’s not just a circle, is just a fucking circle!

I was outraged. Certainly, a megagon will necessarily render on the screen as a circle, but Wikipedia images can be vector files. As an SVG, it can be a real megagon behind the scenes. It’s totally unacceptable to have the SVG internally represent the data as a simple circle.

I resolved that I would fix this. Probably there was some reason why the Wikipedians had taken this cowardly cop-out - perhaps normal vector editing software can’t do it - but I wasn’t going to let that stop me.

First, I checked that I couldn’t just do it the obvious easy way and make the shape with Inkscape.

It couldn’t do more than 1024 sides. That’s fine, SVG is a simple enough XML-based format, you can write Python code to generate the correct file directly. That’s quite easy to do, and I did it quite easily.

The problem is, the resulting file was huge (for an SVG), at 21MB.

Visualising it was a little tricky.

Inkscape was happy to open the file, but I suspect it was taking some shortcuts.

The GIMP can also open SVGs, but did not prove strong enough to contain the power of The True Megagon.

Firefox could display it correctly, but only very very slowly, and with much whirring of fans.

When I tried to upload the file to Wikipedia to be the image for the Megagon page, they threw me in Noob Jail. I don’t blame them for this; I expect the overwhelming majority of the time that a brand new user account tries to upload a weirdly large file, it’s correct to not let them do that.

I later learned that Wikipedia’s SVG renderer won’t even try to render any file bigger than 8MB.

I couldn’t think of any way to get the file down below that limit. I could zip it of course, but that wouldn’t help, as the renderer needs to operate on the uncompressed file. I could make the individual coordinate numbers shorter, by rounding them to fewer decimal places, but that wouldn’t work either: the vertices of the megagon are so close together that you really need all of the decimal places available. Round off too many, and adjacent vertices start to fall on exactly the same point, which makes it not a real megagon at all.

And even if I could get the file small enough somehow, Wikipedia’s renderer would almost certainly fail anyway, like Inkscape or The GIMP.

Hope was lost. My goal, my dream of bringing The True Megagon to The People, was truly beyond my reach. I was defeated.

At dawn, look to the East

More than a year later, I was revisiting the site of my defeat, as I often did, idly picking at an old wound that might eventually heal one day if I could just stop opening it up again.

Imagine my surprise when I found that the page had been updated. A new file had replaced the acursed circle, and this one claimed the Mantle of the Rightful King, the True Megagon, foretold in legend!

Furthermore, imagine my astonishment at seeing the file size! Less than 8 megabytes, yes, less than 8 kilobytes! A miniscule 4KB file!

This was a work of deeper wizardry than any I knew of.

And on the file listing, these words appear:

Source: https://neizod.dev/locales/2021-05-27-megagon-and-sum-of-product-upto-index.html

I followed the link of course, and found this:

After asking Google to decipher this, I started to comprehend what had happened.

Our hero, who goes by the name Neizod, has since uploaded an English translation, so I will commend you to his blog rather than duplicating his explanation here. I assure you, it is very clever.

I'm delighted to have my normal narrative violated. Behold a new cool person!

theconcealedweapon

physicallyimprobable

Reminds me of my favorite one-off gag from @dresdencodak's lovely Dark Science:

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